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Concert tickets are sold £.ther at $100 or at $60 each, and the revenue from the sale of these tickets is the same as if all tickets were sold at $90. What is the ratio of the number of $100 tickets sold to the number of $60 tickets sold?

Concert tickets are sold £ £ .ther at $100 \$ 100 or at $60 \$ 60 each, and the revenue from the sale of these tickets is the same as if all tickets were sold at $90 \$ 90 . What is the ratio of the number of $100 \$ 100 tickets sold to the number of $60 \$ 60 tickets sold?

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Q. Concert tickets are sold £ £ .ther at $100 \$ 100 or at $60 \$ 60 each, and the revenue from the sale of these tickets is the same as if all tickets were sold at $90 \$ 90 . What is the ratio of the number of $100 \$ 100 tickets sold to the number of $60 \$ 60 tickets sold?
  1. Define Variables: Let's call the number of $\$100100 tickets xx and the number of $\$6060 tickets yy. The total revenue from xx tickets at $\$100100 each is 100x100x, and the total revenue from yy tickets at $\$6060 each is 60y60y. If all tickets were sold at $\$9090 each, the total revenue would be xx11. So, the equation is xx22.
  2. Simplify Equation: Now, let's simplify the equation. Distribute the 9090 on the right side to get 100x+60y=90x+90y100x + 60y = 90x + 90y.
  3. Isolate Variables: Subtract 90x90x and 60y60y from both sides to isolate the variables on one side. We get 100x−90x+60y−60y=90x−90x+90y−60y100x - 90x + 60y - 60y = 90x - 90x + 90y - 60y, which simplifies to 10x=30y10x = 30y.
  4. Solve for xx: Divide both sides by 1010 to simplify the ratio. We get x=3yx = 3y.
  5. Final Ratio: The ratio of $100\$100 tickets to $60\$60 tickets is x:yx:y, which is 3y:y3y:y. Simplify the ratio by dividing both terms by yy to get 3:13:1.

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